King David had red-hair.
1-Samuel 16:12 So he [Samuel the Prophet] sent and brought him [David] in. Now he was red-haired [Hebrew "admoni"] , with beautiful eyes, and of goodly appearance. And the LORD said, “Arise, anoint him; for this is the one!” 13 Then Samuel took the horn of oil and anointed him in the midst of his brothers; and the Spirit of the LORD came upon David from that day forward. So Samuel arose and went to Ramah.
1-Samuel 17:42 And when the Philistine [i.e. Goliath] looked about and saw David, he disdained him; for he was only a youth, red-haired [Hebrew "admoni"] and of goodly appearance.
David had many children and so did his descendants.
It would not have taken long for a clan in its own right of this family to have emerged.
2-Samuel 8:18....David’s sons were chief ministers.
David wrote the Book of Psalms and was a musician. He and his descendants were occupied with preparing, building, and maintaining the Temple. David had been both a warrior and an introspective mystic. The Levites served in the Temple. A good portion of them were musicians, playing musical instruments, and singing the Psalms of David.
The interests and preoccupations of the Levites and the Clan of David overlapped. Perhaps they intermixed?
It was prophesied that in the future BOTH the descendants of David and the Levites would be multiplied exceedingly.
Jeremiah (NASB) 33:19 The word of the LORD came to Jeremiah, saying, 20 “Thus says the LORD, ‘If you can break My covenant for the day and My covenant for the night, so that day and night will not be at their appointed time, 21 then My covenant may also be broken with David My servant so that he will not have a son to reign on his throne, and with the Levitical priests, My ministers. 22 As the host of heaven cannot be counted and the sand of the sea cannot be measured, so I will multiply the descendants of David My servant and the Levites who minister to Me.’”